Question: $74$ people attended a baseball game. Everyone there was a fan of either the home team or the away team. The number of home team fans was $81$ less than $4$ times the number of away team fans. How many home team and away team fans attended the game?
Explanation: Let $x$ equal the number of home team fans and $y$ equal the number of away team fans. The system of equations is then: ${x+y = 74}$ ${x = 4y-81}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${4y-81}$ for $x$ in the first equation. ${(4y-81)}{+ y = 74}$ Simplify and solve for $y$ $ 4y-81 + y = 74 $ $ 5y-81 = 74 $ $ 5y = 155 $ $ y = \dfrac{155}{5} $ ${y = 31}$ Now that you know ${y = 31}$ , plug it back into ${x = 4y-81}$ to find $x$ ${x = 4}{(31)}{ - 81}$ $x = 124 - 81$ ${x = 43}$ You can also plug ${y = 31}$ into ${x+y = 74}$ and get the same answer for $x$ ${x + }{(31)}{= 74}$ ${x = 43}$ There were $43$ home team fans and $31$ away team fans.